{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import poisson\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "poissonContainer = {}\n",
    "\n",
    "def poisson_distribution(n, lam):\n",
    "    global poissonContainer\n",
    "    if str(n) + \",\" + str(lam) not in poissonContainer:\n",
    "        poissonContainer[str(n) + \",\" + str(lam)] = poisson.pmf(n, lam)\n",
    "    return poissonContainer[str(n) + \",\" + str(lam)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "MAX_CAR = 20\n",
    "\n",
    "RENT_LAM_FIRST_PLACE = 3\n",
    "RENT_LAM_SECOND_PLACE = 4\n",
    "RETURN_LAM_FIRST_PLACE = 3\n",
    "RETURN_LAM_SECOND_PLACE = 2\n",
    "\n",
    "RENT_REWARD_PER_CAR = 10\n",
    "\n",
    "TRANSFER_REWARD_PER_CAR = -2\n",
    "\n",
    "DISCOUNT = 0.9\n",
    "\n",
    "MAX_TRANSFER_NUMBER = 5\n",
    "\n",
    "POISSON_UPPER_BOUND = 11\n",
    "\n",
    "stateValue = np.zeros(shape = (MAX_CAR + 1, MAX_CAR + 1))\n",
    "actionMatrix = np.zeros(shape = (MAX_CAR + 1, MAX_CAR + 1), dtype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def action_value(firstNumber, secondNumber, action, stateValue):\n",
    "\n",
    "    reward = 0\n",
    "    action1 = action\n",
    "    if action > 0:\n",
    "        if action > firstNumber:\n",
    "            action = firstNumber\n",
    "    else:\n",
    "        if abs(action) > secondNumber:\n",
    "            action = -secondNumber\n",
    "    nextDayFirstNumber = min(max(firstNumber - action, 0), MAX_CAR)\n",
    "    nextDaySecondNumber = min(max(secondNumber + action, 0), MAX_CAR)\n",
    "    reward += abs(action1) * TRANSFER_REWARD_PER_CAR\n",
    "\n",
    "    for i in range(POISSON_UPPER_BOUND):\n",
    "        for j in range(POISSON_UPPER_BOUND):\n",
    "            prob = poisson_distribution(i, RENT_LAM_FIRST_PLACE) * poisson_distribution(j, RENT_LAM_SECOND_PLACE)\n",
    "            validRentFirst = min(nextDayFirstNumber, i)\n",
    "            validRentSecond = min(nextDaySecondNumber, j)\n",
    "            reward += prob * (validRentFirst + validRentSecond) * RENT_REWARD_PER_CAR\n",
    "            nextDayAfterRentFirstNumber = nextDayFirstNumber - validRentFirst\n",
    "            nextDayAfterRentSecondNumber = nextDaySecondNumber - validRentSecond\n",
    "\n",
    "\n",
    "            for p in range(POISSON_UPPER_BOUND):\n",
    "                for q in range(POISSON_UPPER_BOUND):\n",
    "                    probReturn = poisson_distribution(p, RETURN_LAM_FIRST_PLACE) * poisson_distribution(q, RETURN_LAM_SECOND_PLACE)\n",
    "                    probTotal = prob * probReturn\n",
    "                    nextDayStateFirst = min(nextDayAfterRentFirstNumber + p, MAX_CAR)\n",
    "                    nextDATStateSecond = min(nextDayAfterRentSecondNumber + q, MAX_CAR)\n",
    "                    reward += probTotal * DISCOUNT * stateValue[nextDayStateFirst][nextDATStateSecond]\n",
    "    return reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policyEvaluation(actionMatrix, stateValue, theta):\n",
    "    delta = 1e9\n",
    "    while delta > theta:\n",
    "        delta = 0\n",
    "        oldValue = np.array(stateValue)\n",
    "        for i in range(MAX_CAR + 1):\n",
    "            for j in range(MAX_CAR + 1):\n",
    "                stateValue[i][j] = action_value(i, j, actionMatrix[i][j], oldValue)\n",
    "                delta = max(delta, abs(oldValue[i][j] - stateValue[i][j]))\n",
    "        print(delta)\n",
    "    return stateValue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def drawPolicyFig(actionMatrix, number):\n",
    "    colorContainer = {-5:\"black\", -4:'blue', -3:'burlywood', -2:'coral', -1:'yellow', 0:'gray', 1:'gold', 2:'green', 3:'orange', 4:'purple', 5:'red'}\n",
    "    for i in range(21):\n",
    "        for j in range(21):\n",
    "            plt.plot(j, i,\n",
    "                    color = colorContainer[int(actionMatrix[i][j])],\n",
    "                    marker='.',  # 点的形状为圆点\n",
    "                    markersize=10,  # 点设置大一点，看着清楚\n",
    "                    linestyle='-.')  # 线型为点划线\n",
    "    plt.savefig(\"policyIteration\" + str(number) + \".png\")\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "def policyImprovement(actionMatrix, stateValue, theta):\n",
    "    policyStable = False\n",
    "    drawPolicyFig(actionMatrix, 0)\n",
    "    stateValue = policyEvaluation(actionMatrix, stateValue, theta)\n",
    "    number = 1\n",
    "    while policyStable == False:\n",
    "        policyStable = True\n",
    "        oldAction = np.array(actionMatrix)\n",
    "        for i in range(MAX_CAR + 1):\n",
    "            for j in range(MAX_CAR + 1):\n",
    "                tmpValue = action_value(i, j, actionMatrix[i][j], stateValue)\n",
    "                for k in range(-MAX_TRANSFER_NUMBER, MAX_TRANSFER_NUMBER + 1):\n",
    "                    kValue = action_value(i, j, k, stateValue)\n",
    "                    if kValue > tmpValue:\n",
    "                        actionMatrix[i][j] = k\n",
    "                        tmpValue = kValue\n",
    "                if oldAction[i][j] != actionMatrix[i][j]:\n",
    "                    policyStable = False\n",
    "        if policyStable == False:\n",
    "            stateValue = policyEvaluation(actionMatrix, stateValue, theta)\n",
    "            drawPolicyFig(actionMatrix, number)\n",
    "            number += 1\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "69.54493820103355\n",
      "62.37569817769415\n",
      "55.93290661797258\n",
      "49.99268205860983\n",
      "44.22803022589565\n",
      "38.57585707645126\n",
      "33.25853674756041\n",
      "28.518901970629656\n",
      "24.46789348460959\n",
      "21.088423894080904\n",
      "18.293680573844654\n",
      "51.14904907518968\n",
      "35.937663756755626\n",
      "20.02039238081943\n",
      "12.696950948268352\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.139816725525407\n"
     ]
    },
    {
     "data": {
      "image/png": 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mrDVjmxPIbpUZmyDrsfOyIcfWnMvLZqUajT6Q3SozNkHWY+dlQ46tOZeXzUo1Gn0gu1VmrKzHTs3GWrfmLDN2cQLZrTJjZT12ajbWujVnmbFCCCEaIDNWCCG6GDV6IYSoOJmEKTO7m2R92KPu/s5022rgQWA9cBD4kLu/1CB7PfDH6d0/cfd78pfdgBjXfZUZK+uxwGysdWvO4czYr5MsH3hvzbZbgO+5+2fM7Jb0/idqQ+kvg9uAQcCBfWb2cKNfCLmIcd1XmbGyHnW8NOc2zDkLmZ7F3R8FjtVtvgZYeHV+D/D+BtGtwF53P5Y2973AVcsrdRFiXPdVZqysxwKzsdatOXeeGXueu0+ltw+TLAZezwDwfM39Q+m2N2FmO8xszMzGpqenW6skxnVfZca2lA05dozZkGNrzuVls9KWvws8uUYz13Wa7r7L3QfdfbCvr6+1cIzrvsqMbSkbcuwYsyHH1pzLy2YlT6M/Ymb9AOnnow32mQTW1dy/IN3WXmJc91VmrKzHArOx1q05BzZjzWw98J2aq24+B7xY82bsanf/eF1mNbAP2Jxu2g+8y93rz/efQkxmbC67VWasrMcCs7HWrTkHMmPN7AFgC7AGOEJyJc23gb8GfgV4juTyymNmNgjsdPc/TLM3Ap9Mn+oOd//LpcaTGSuEEK2hf4EghBAVR/8CQQghuphqLCVInOu+5jJb8+ZlxlY+G2vdmrPWjG1IjOu+5jJb8+ZlxlY+G2vdmrPWjG1KjOu+5jJb8+ZlxlY+G2vdmnPnmbEdQ4zrvuYyW/PmZcZWPhtybM25vGxWKtHoY1z3NZfZmjcvM7by2ZBja87lZbNSiUYf47qvuczWvHmZsZXPxlq35qw1YxclxnVfc5mtefMyYyufjbVuzVlrxgohhGiAhCkhhOhi1OiFEKLiVEKYAsKt3RrQjM1jt8qMrX421ro1Z5mxjQm1dmtAMzaP3SoztvrZWOvWnGXGNifU2q0Bzdg8dqvM2OpnY61bc5YZ25xQa7cGNGPz2K0yY6ufDTm25lxeNivVaPSh1m4NaMbmsVtlxlY/G3Jszbm8bFaW3ejN7B1mNl7z8YqZ3Vy3zxYze7lmn1tzV9yIUGu3BjRj89itMmOrn421bs25g81YM1tBsuj3kLs/V7N9C/Axd7+6ledbljAVau3WgGZsHrtVZmz1s7HWrTl3qBlrZlcCt7n7r9dt30JZjV4IIbqYMszY7cADTR57j5k9bmYjZnZxsycwsx1mNmZmY9PT020qSwghRO5Gb2Y9wPuAv2nw8H7gbe5+CfAl4NvNnsfdd7n7oLsP9vX15S1LCCFESjuEqWFgv7sfqX/A3V+pub3bzP7czNa4+wttGPdUAhmqobJAlHarrEcdryKzsdYdgxl7LU1O25jZWuCIu7uZXUryF8SLbRjzVAIZqqGyQJR2q6xHHS/Nuf1zzkKuZzGzXuC9wLdqtu00s53p3Q8CT5rZ48AXge1exP9FDmSohsoCUdqtsh51vIrMxlp3x5ux7j7j7ue6+8s12+5y97vS23e6+8Xufom7v9vd/zFvwQ0JZKiGygJR2q2yHsvLhhxbcy4vm5WuN2PzGKqhskCUdqusx/KyIcfWnMvLZqUajT6QoRoqC0Rpt8p61PEqMhtr3dGYse2mbDM2j6EaKgtEabfKetTxKjIba91RmLHtRmasEEK0htaMFUKILkaNXgghKk41lhIkoKEaaN3WvPlYDcAY69bx0pyLzGahEo0+mKEaaN3WvPlYDcAY69bx0pyjN2M7hWCGaqB1W/PmYzUAY6xbx0tzLjKblUo0+mCGaqB1W/PmYzUAY6xbx6u8bMixZcaWQDBDNdC6rXnzsRqAMdat41VeNuTYMmNLIJihGmjd1rz5WA3AGOvW8dKci8xmpTLCVDBDNdC6rXnzsRqAMdat46U5F5ldQGasEEJUHJmxQgjRxeS+jt7MDgLHgTngZP1vFDMz4AvANuAXwA3uvj/vuG8ilLgUSFrKm48xG2vdOl6ac5HZLLRLmPrNRdaBHQYuSj+GgK+kn9tHKHEpkLSUNx9jNta6dbw0524Rpq4B7vWEHwJvNbP+to4QSlwKJC3lzceYjbVuHS/NuchsVtrR6B14xMz2mdmOBo8PAM/X3D+UbjsFM9thZmNmNjY9Pd1aBaHEpUDSUt58jNmQY8eYDTm25lxeNivtaPSXuftmklM0N5nZ5ct5Enff5e6D7j7Y19fXWjiUuBRIWsqbjzEbcuwYsyHH1pzLy2Yld6N398n081HgIeDSul0mgXU19y9It7WPUOJSIGkpbz7GbKx163hpzkVms5LrOnoz6wVOc/fj6e29wO3u/t2aff4d8FGSq26GgC+6e/0vg1NY1nX0ocSlQNJS3nyM2Vjr1vHSnIvMLlCYMGVmF5K8iofkCp7/5e53mNlOAHe/K7288k7gKpLLK//A3Rft4hKmhBCiNRZr9Lkur3T3Z4FLGmy/q+a2AzflGUcIIcTykRkrhBAVpxIrTAFaVi+SujVnHa8is/HWPQeMAAeATSQXMbbwDw6XoBqNXsvqRVG35qzjpTk3Yg7YCowCM0AvyXUre2hXs6/GqRstqxdF3ZqzjleR2XjrHiFp8mn/4kR6P+OyohmoRqPXsnqlja05x5ENObbm3Fo2OV1T17+YAcYzZLNRjUavZfVKG1tzjiMbcmzNubVsck6+rn/RC2zMkM1GNRq9ltWLom7NWceryGy8dQ+TnJNP+xer0vsZlxXNQHVWmNKyelHUrTnreBWZjbfuhatuxkleybd+1Y2WEhRCiIqjpQSFEKKLUaMXQoiKUw1hijhtuG40ADVnHa+lyWuJ5snHmF2aSjT6GG24bjQANWcdr+It0Tz5GLPZqMSpmxhtuG40ADVnHa+lyWuJ5snHmM1GJRp9jDZcNxqAmnN52ZBjh7VE8+RjzGajEo0+RhuuGw1Azbm8bMixw1qiefIxZrOx7EZvZuvM7Ptm9rSZPWVmf9Rgny1m9rKZjacft+YrtzEx2nDdaABqzjpeS5PXEs2TjzGbjWULU2bWD/S7+34zOxvYB7zf3Z+u2WcL8DF3v7qV516OMBWjDdeNBqDmrOO1NHkt0Tz5GLMJpZixZva3wJ3uvrdm2xZKavRCCNHNFG7Gmtl6khNNow0efo+ZPW5mI2Z28SLPscPMxsxsbHp6uh1lCSGEoA2N3sxWAd8Ebnb3V+oe3g+8zd0vAb4EfLvZ87j7LncfdPfBvr6+vGUJIYRIySVMmdnpJE3+fnf/Vv3jtY3f3Xeb2Z+b2Rp3fyHPuI2I0QDsRuuxG+cc1piM0fTMOef5OXhmPxz+F1j7drhoM5yWMR9jNgPLbvRmZsDXgJ+4+5822WctcMTd3cwuJfkL4sXljtmMGA3AbrQeu3HOYY3JGE3PnHOen4Nv/DeYfAZmX4eeM2DgIvj925ZunDFmM5Ln1M2vA78P/FbN5ZPbzGynme1M9/kg8KSZPQ58EdjuBfxf5BgNwG60HrtxzmGNyRhNz5xzfmZ/2jBfS/KzryX3n9lfzWxGlt3o3f0H7m7u/mvuvjH92O3ud7n7Xek+d7r7xe5+ibu/293/sW2V1xCjAdiN1mM3zjmsMRmj6Zlzzof/JXlVXMvs63D4YDWzGZEZG2E25Niac2vZsMZkjKZnzjmvfXty6qOWnjNg7fpqZjNSiUYfowHYjdZjN845rDEZo+mZc84XbU7Ob/ecmeR7zkzuX7S5mtmMVGYpwRgNwG60HrtxzmGNyRhNz5xzfuMKloPJq+JlXf0SUTZFa8YKIUTF0ZqxQgjRxajRCyFExanEUoIQpzHZjZZoyDlHaXrmNSZjND0Dztl9nlenn+X140c44+zzOKvvQsyyfX+FymahEo0+RmOyGy3RkHOO0vTMa0zGaHoGnLP7PIfHHuT1l3+Oz/0SW3E6Z7zlfNYOfnjJphsqm5VKnLqJ0ZjsRks05JyjND3zGpMxmp4B5/zq9LNvNFsAn/slr7/8c16dfrZjs1mpRKOP0ZjsRks05JyjND3zGpMxmp4B5/z68SNvNNsFfO6XvH78SMdms1KJRh+jMdmNlmjIOUdpeuY1JmM0PQPO+Yyzz8NWnH7KNltxOmecfV7HZrNSiUYfozHZjZZoyDlHaXrmNSZjND0Dzvmsvgs54y3nv9F0F86Vn9V3Ycdms1IZYSpGY7IbLdGQc47S9MxrTMZoegacc8xX3ciMFUKIiiMzVgghuhg1eiGEqDh514y9CvgCyQnHr7r7Z+oePwO4F3gXyRKCH3b3g3nGbEaMpmc3mrHRroEaqSUa4znnvOerQ409NwcjI3DgAGzaBMPDsCLjlypPNgt51oxdAXwZeC9wCHjMzB5296drdvsI8JK7bzCz7cBngQ/nKbgRMZqe3WjGRrsGaqSWaIymZ15LNNTYc3OwdSuMjsLMDPT2wtAQ7NmzdMPOk81KnlM3lwIT7v6su88CfwVcU7fPNcA96e3/DVyRLireVmI0PbvRjI12DdRILdEYTc+8lmiosUdGkkZ94gS4J59HR5PtRWazkqfRDwDP19w/lG5ruI+7nwReBs5t9GRmtsPMxsxsbHp6uqVCYjQ9u9GMjXYN1Egt0RhNz7yWaKixDxxIXo3XMjMD4+NLRnNls9Ixb8a6+y53H3T3wb6+vpayMZqe3WjGRrsGaqSWaIymZ15LNNTYmzYlp1xq6e2FjRuXjObKZiVPo58E1tXcvyDd1nAfM1sJvIXkTdm2EqPp2Y1mbLRroEZqicZoeua1REONPTycnFdftQrMks9DQ8n2IrNZWbYwlTbunwFXkDT0x4Dfdfenava5CfjX7r4zfTP2A+7+oaWeW2ZsNuKsO9I1UCO1RGO8cib2q27Gx5NX48u56mY52QUKM2PNbBvwZyQ/LXe7+x1mdjsw5u4Pm9mZwDdI/m4+Bmx39yXf2ZAZK4QQrbFYo891Hb277wZ21227teb2a8C/zzOGEEKIfHTMm7FCCCGKQY1eCCEqjhq9EEJUHDV6IYSoOB35/+jNbBp4bpnxNcALbSynXaiu1lBdraG6WqOKdb3N3Rvaph3Z6PNgZmPNLjEKiepqDdXVGqqrNbqtLp26EUKIiqNGL4QQFaeKjX5X6AKaoLpaQ3W1hupqja6qq3Ln6IUQQpxKFV/RCyGEqEGNXgghKk60jd7MrjKz/2tmE2Z2S4PHzzCzB9PHR81sfQk1rTOz75vZ02b2lJn9UYN9tpjZy2Y2nn7c2ui5CqjtoJk9kY75pn8NaglfTI/Xj80s2z89z1fTO2qOw7iZvWJmN9ftU8rxMrO7zeyomT1Zs221me01s2fSz+c0yV6f7vOMmV1fQl2fM7Ofpl+nh8zsrU2yi37NC6jr02Y2WfO12tYku+jPbgF1PVhT00EzG2+SLfJ4NewNpX2PuXt0HyT/FvmfgQuBHuBx4F/V7fOfgbvS29uBB0uoqx/YnN4+m+T/9dfXtQX4ToBjdhBYs8jj20j+WbsB7wZGA3xND5NIH6UfL+ByYDPwZM22/w7ckt6+Bfhsg9xq4Nn08znp7XMKrutKYGV6+7ON6sryNS+grk8DH8vwdV70Z7fdddU9/nng1gDHq2FvKOt7LNZX9B2zMHkt7j7l7vvT28eBn/DmdXQ7lWuAez3hh8Bbzay/xPGvAP7Z3ZdrROfC3R8lWTOhltrvoXuA9zeIbgX2uvsxd38J2AtcVWRd7v6IJ2swA/yQZHW3UmlyvLKQ5We3kLrSn/8PAQ+0a7ysLNIbSvkei7XRt3Vh8iJITxVtAkYbPPweM3vczEbM7OKSSnLgETPbZ2Y7Gjye5ZgWyXaa/wCGOF4A57n7VHr7MNBo8dDQx+1Gkr/EGrHU17wIPpqeUrq7yWmIkMfrN4Aj7v5Mk8dLOV51vaGU77FYG31HY2argG8CN7v7K3UP7yc5PXEJ8CXg2yWVdZm7byZZP+8mM7u8pHGXxMx6gPcBf9Pg4VDH6xQ8+Ru6o65FNrNPASeB+5vsUvbX/CvAr5Ks0zhFcpqkk7iWxV/NF368FusNRX6PxdroO2Zh8nrM7HSSL+T97v6t+sfd/RV3P5He3g2cbmZriq7L3SfTz0eBh0j+hK4lyzEtimFgv7sfqX8g1PFKObJw+ir9fLTBPkGOm5ndAFwN/F7aIN5Ehq95W3H3I+4+5+7zwF80GS/U8VoJfAB4sNk+RR+vJr2hlO+xWBv9Y8BFZvb29NXgduDhun0eBhbenf4g8A/NfiDaRXoO8GvAT9z9T5vss3bhvQIzu5Tka1DoLyAz6zWzsxduk7yZ92Tdbg8D/8ES3g28XPMnZdE0faUV4njVUPs9dD3wtw322QNcaWbnpKcqrky3FYaZXQV8HHifu/+iyT5Zvubtrqv2PZ3faTJelp/dIvht4KfufqjRg0Ufr0V6QznfY0W8w1zGB8lVIj8jeQf/U+m220m++QHOJDkVMAH8CLiwhJouI/nT68fAePqxDdgJ7Ez3+SjwFMnVBj8E/k0JdV2Yjvd4OvbC8aqty4Avp8fzCWCwpK9jL0njfkvNttKPF8kvminglyTnQD9C8p7O94BngL8HVqf7DgJfrcnemH6fTQB/UEJdEyTnbBe+xxauLjsf2L3Y17zgur6Rfu/8mKSB9dfXld5/089ukXWl27++8D1Vs2+Zx6tZbyjle0z/AkEIISpOrKduhBBCZESNXgghKo4avRBCVBw1eiGEqDhq9EIIUXHU6IUQouKo0QshRMX5/85Muo7NIuYLAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.94723796011715\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.657336785788573\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.598156728201161\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "policyImprovement(actionMatrix, stateValue, 20)"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "494899efd6527d56ea7f55c588d0081523a17dc3a9ff1107f3394ad815ff2527"
  },
  "kernelspec": {
   "display_name": "Python 3.7.7 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
